From Pareto Fronts to Statistical Evidence: Selective Inference for Models and Policies

Multi-objective evaluation often uses the same noisy data both to select a Pareto shortlist and to support claims about the selected models or policies. This creates a post-selection problem: uncertainty statements that ignore how the shortlist was chosen need not provide the advertised reliability for the report that is actually published. We develop report-conditional inference for complete Pareto reports around a structural observation: the reported candidates themselves provide the dominance witnesses needed to reconstruct the entire selection event. Along an inferential line, each required dominance relation occupies an interval, so a report of size $s$ among $K$ candidates can be reconstructed from only $s(K-1)$ directed relations. This yields support construction in $O(Ksd+Ks\log (Ks+1))$ with near-optimal dependence on $Ks$ for fixed $d$ and sparse reports. Under joint Gaussianity, the reconstructed support gives exact conditional inference and enables scalar carving, which reuses selection data while preserving the same reported labels. Across Gaussian designs, model libraries, and policy evaluations, the method maintains report-level calibration while recovering substantially more information than matched splitting. In the primary image setting, carving reduces mean paired interval width by 33.6%; in a 1,024-configuration Bank library, report-sensitive reconstruction yields a $1.95\times$ end-to-end median acceleration over all-pair compression.